Cutting inserts and cutting tool systems having sinusoidal and helical cutting edges

ABSTRACT

A cutting tool system is designed to have a combined sinusoidal-shaped and helical-shaped cutting edge formed by an assembly of aligned common cutting inserts each having a sinusoidal and helical cutting edge.

CROSS-REFERENCE TO EARLIER PATENT APPLICATION

This patent application is a continuation patent application toco-pending U.S. patent application Ser. No. 13/206,558 filed Aug. 10,2011 to X. Daniel Fang et al. for CUTTING INSERTS AND CUTTING TOOLSYSTEMS HAVING SINUSOIDAL AND HELICAL CUTTING EDGES, and applicantshereby claim the benefit under 35 USC 120 of such parent patentapplication (U.S. Ser. No. 13/206,558, filed Aug. 10, 2011). Applicantsfurther hereby incorporate by reference herein the entirety of suchparent patent application (U.S. Ser. No. 13/206,558, filed Aug. 10,2011).

TECHNICAL FIELD

This disclosure generally relates to cutting tools, including cuttingtool holders and cutting inserts. In particular, this disclosure relatesto indexable and replaceable cutting inserts and to tool holdersconfigured to engage and secure indexable and replaceable cuttinginserts such as, for example, inserts and holders for rotary machiningtool systems.

BACKGROUND

Indexable cutting inserts for cutting tools include, for example,cutting inserts made of carbide, ceramic, coated carbide, coatedceramic, or other hard materials. Cutting inserts generally have aunitary structure and one or more cutting edges located at variouscorners or around peripheral edges of the inserts. Indexable cuttinginserts are mechanically secured to a tool holder, but the inserts areadjustable and removable in relation to the tool holder. Indexablecutting inserts may be readily re-positioned (i.e., indexed) to presenta new cutting edge to engage a workpiece, or indexable cutting insertsmay be replaced in a tool holder when the cutting edges dull orfracture, for example. In this manner, indexable insert cutting toolsare modular cutting tool assemblies that include at least one cuttinginsert and a tool holder.

Indexable insert cutting tool systems comprising a tool holder and oneor more replaceable and/or indexable cutting inserts are generally moreeconomical than unitary cutting tools. This is so because indexableinsert cutting tool systems allow for the indexing and replacement ofworn and/or damaged cutting edges/surfaces, whereas unitary cuttingtools require scrapping the entire cutting tool when worn out ordamaged. However, for rotary cutting tools that require complex cuttingedge configurations along the longitudinal axis of the tool, such as,for example, milling and other rotary machining tools, unitary cuttingtools are less complex to design and manufacture than indexable insertcutting tool systems. This is so because the cutting edge configurationof an indexable insert cutting tool system must be formed by an assemblyof separate cutting inserts as opposed to a continuous and unitary pieceof shaped material.

SUMMARY

In a non-limiting embodiment, a cutting insert comprises at least onesinusoidal and helical cutting edge.

In another non-limiting embodiment, a cutting tool system comprises atool holder and a plurality of common cutting inserts. The tool holdercomprises a plurality of common insert pockets positioned in a helicalorientation about a longitudinal axis of the tool holder. The pluralityof common cutting inserts are removably attachable to the plurality ofcommon insert pockets in the tool holder. When so attached, theplurality of common cutting inserts form at least one cutting flute onthe tool holder. The at least one cutting flute comprises a helicalgrouping of common cutting inserts positioned in the insert pockets. Thecommon cutting inserts each comprise at least one sinusoidal and helicalcutting edge. The at least one cutting flute comprises a sinusoidal andhelical cutting edge positioned about the longitudinal axis of the toolholder. The sinusoidal and helical cutting edge of the at least onecutting flute is formed by alignment of the individual sinusoidal andhelical cutting edges of the common cutting inserts that comprise the atleast one cutting flute.

In another non-limiting embodiment, a cutting tool system comprises atool holder and a plurality of common cutting inserts. The tool holdercomprises two or more series of common insert pockets. Each series ofcommon insert pockets is positioned in a helical orientation about alongitudinal axis of the tool holder. The plurality of common cuttinginserts are removably attachable to the common insert pockets in thetool holder. When so attached, the plurality of common cutting insertsform two or more cutting flutes on the tool holder. The two or morecutting flutes each comprise a helical grouping of the common cuttinginserts positioned in the insert pockets. The common cutting insertseach comprise at least one sinusoidal and helical cutting edge. The twoor more cutting flutes each comprise a sinusoidal and helical cuttingedge positioned about the longitudinal axis of the tool holder. Thesinusoidal and helical cutting edges of the two or more cutting flutesare formed by alignment of the individual sinusoidal and helical cuttingedges of the common cutting inserts that comprise the two or morecutting flutes.

It is understood that the invention disclosed and described in thisspecification is not limited to the embodiments summarized in thisSummary.

BRIEF DESCRIPTION OF THE DRAWINGS

Various features and characteristics of the non-limiting andnon-exhaustive embodiments disclosed and described in this specificationmay be better understood by reference to the accompanying figures, inwhich:

FIG. 1 is a three-dimensional perspective view of a cutting insertcomprising two indexable cutting edges, each cutting edge comprising asinusoidal and helical geometric shape;

FIG. 2 is an end view of the cutting insert shown in FIG. 1 (viewed fromthe end shown in perspective in FIG. 1);

FIG. 3 is a top view, together with two detailed views, of the cuttinginsert shown in FIGS. 1 and 2;

FIG. 4 is a side view of the cutting insert shown in FIGS. 1-3 (viewedfrom the left side of the cutting insert as shown in FIG. 3);

FIG. 5 shows schematic diagrams of the cutting insert shown in FIGS. 1-4illustrating the sinusoidal and helical cutting edges of the cuttinginsert, in which FIG. 5(a) is a schematic end view and FIG. 5(b) is aschematic top view;

FIG. 6 shows schematic diagrams of the cutting insert shown in FIGS. 1-5illustrating the geometric positioning of the cutting insert relative toa coordinate system, positioned as if the cutting insert were secured ona rotary tool holder (not shown), in which FIG. 6(a) is a top viewschematic diagram and FIGS. 6(b) and 6(c) are perspective view schematicdiagrams;

FIG. 7 shows schematic diagrams illustrating curves derived to establisha mathematical design model for the sinusoidal and helical cutting edgesof the insert shown in FIGS. 1-6, in which the curves shown in FIGS.7(a), 7(b), and 7(c) correspond to the cutting insert positioning shownin FIGS. 6(a), 6(b), and 6(c), respectively;

FIG. 8 shows schematic diagrams illustrating the relative positioning ofa series of common cutting inserts (as shown in FIGS. 1-6), positionedas if the cutting inserts were assembled and secured to a rotary toolholder (not shown) to form a cutting flute comprising the series ofcutting inserts and having a cutting edge comprising a sinusoidal andhelical geometric shape, in which FIG. 8(a) is a side view schematicdiagram of the cutting flute and FIG. 8(b) is an end view schematicdiagram of the cutting flute;

FIG. 9 shows three views of a cutting insert having two indexablecutting edges and configured to be used as an end-face cutting insert incombination with the cutting inserts as shown in FIGS. 1-6 and 8, inwhich FIG. 9(a) is a top view of the end cutting insert, FIG. 9(b) is aview from the direction indicated by arrow HH in FIG. 9(a), and FIG.9(c) is a view from the direction indicated by arrow VV in FIG. 9(a);

FIG. 10 shows schematic diagrams illustrating the relative positioningof a series of common cutting inserts (as shown in FIGS. 1-6 and 8) anda different end-face cutting insert (as shown in FIG. 9), positioned asif the cutting inserts were assembled and secured to a rotary toolholder (not shown) to form a cutting flute comprising the series ofcommon cutting inserts and having a cutting edge comprising a sinusoidaland helical geometric shape, in which FIG. 10(a) is a side viewschematic diagram of the cutting flute and FIG. 10(b) is an end viewschematic diagram of the cutting flute;

FIG. 11 shows schematic diagrams illustrating the relative positioningof a series of different-sized end-face cutting inserts (similar to theend-face cutting insert shown in FIG. 9), positioned as if the end-facecutting inserts where assembled and secured to a rotary tool holder (notshown) configured to comprise five cutting flutes, in which FIG. 11(a)is a side view schematic diagram of the assembly and FIG. 11(b) is anend view schematic diagram of the assembly;

FIG. 12 shows schematic views illustrating the relative positioning offive cutting flutes, each flute comprising a different-sized end-facecutting insert (as shown in FIGS. 9 and 11) and a series of commoncutting inserts (as shown in FIGS. 1-6 and 8), positioned as if thecutting inserts were assembled and secured to a rotary tool holder (notshown), and each cutting flute having a cutting edge comprising asinusoidal and helical geometric shape, in which FIG. 12(a) is an endview schematic diagram of the five cutting flutes and FIG. 12(b) is aside view schematic diagram of the five cutting flutes;

FIG. 13 shows two views of an indexable insert cutting tool systemcomprising a tool holder comprising five cutting flutes, each cuttingflute comprising a different-sized end cutting insert (as shown in FIGS.9 and 11) and a series of common cutting inserts (as shown in FIGS. 1-6and 8), and each cutting flute having a cutting edge comprising asinusoidal and helical geometric shape, in which FIG. 13(a) is an endview of the cutting tool system and FIG. 13(b) is a side view of thecutting tool system;

FIG. 14 shows three views of a cutting insert comprising four indexablecutting edges, each cutting edge comprising a sinusoidal and helicalgeometric shape, in which FIG. 14(a) is a top view of the cuttinginsert, FIG. 14(b) is a side view of the cutting insert, and FIG. 14(c)is a three-dimensional perspective view of the cutting insert;

FIG. 15 shows schematic diagrams of the cutting insert shown in FIG. 14illustrating the geometrical positioning of the cutting insert relativeto a coordinate system, positioned as if the cutting insert were securedon a rotary tool holder (not shown), in which FIG. 15(a) is a side viewschematic diagram, FIG. 15(b) is a top view schematic diagram, and FIG.15(c) is a perspective view schematic diagram;

FIG. 16 shows schematic diagrams illustrating the relative positioningof a series of common cutting inserts (as shown in FIGS. 14 and 15),positioned as if the cutting inserts were assembled and secured to arotary tool holder (not shown) to form a cutting flute comprising theseries of cutting inserts and having a cutting edge comprising asinusoidal and helical geometric shape, in which FIG. 16(a) is a sideview schematic diagram of the cutting flute and FIG. 16(b) is an endview schematic diagram of the cutting flute;

FIG. 17 shows schematic diagrams illustrating the relative positioningof a common cutting insert having two indexable cutting edges and adifferent end-face cutting insert having two indexable cutting edges,positioned as if the cutting inserts were assembled and secured to arotary tool holder (not shown) to form a cutting flute comprising thecutting inserts and forming a cutting edge comprising a sinusoidal andhelical geometric shape, in which FIG. 17(a) is an end view schematicdiagram of the cutting flute and FIGS. 17(b) and 17(c) are side viewschematic diagrams of the cutting flute;

FIG. 18 shows two views of a cutting insert comprising two indexablecutting edges, each cutting edge comprising a sinusoidal and helicalgeometric shape, in which FIG. 18(a) is a three-dimensional perspectiveview of the cutting insert and FIG. 18(b) is a top view of the cuttinginsert;

FIG. 19 shows two views of a cutting insert comprising two indexablecutting edges, each cutting edge comprising a sinusoidal and helicalgeometric shape, in which FIG. 19(a) is a three-dimensional perspectiveview of the cutting insert and FIG. 19(b) is a top view of the cuttinginsert;

FIG. 20 is a three-dimensional perspective view of a cutting insertsimilar to the cutting insert shown in FIGS. 1-6 and 8 and comprisingtwo indexable sinusoidal and helical cutting edges and notchespositioned along the cutting edges;

FIG. 21(a) is a schematic diagram illustrating the positioning of acutting insert comprising two indexable, sinusoidal, and helical cuttingedges relative to a tool holder and a coordinate system;

FIG. 21(b) is a schematic diagram illustrating the positioning of aseries of common cutting inserts comprising two indexable, sinusoidal,and helical cutting edges relative to a tool holder and a coordinatesystem, in which the series of common cutting inserts form a cuttingflute comprising the cutting inserts and having a cutting edgecomprising a sinusoidal and helical geometric shape; and

FIG. 22 is a schematic diagram of an embodiment of a helix.

The reader will appreciate the foregoing details, as well as others,upon considering the following detailed description of variousnon-limiting and non-exhaustive embodiments according to thisspecification.

DESCRIPTION

Various embodiments are described and illustrated in this specificationto provide an overall understanding of the structure, function,operation, manufacture, and use of the disclosed cutting inserts andcutting tool systems. It is understood that the various embodimentsdescribed and illustrated in this specification are non-limiting andnon-exhaustive. Thus, the invention is not necessarily limited by thedescription of the various non-limiting and non-exhaustive embodimentsdisclosed in this specification. The features and characteristicsillustrated and/or described in connection with various embodiments maybe combined with the features and characteristics of other embodiments.Such modifications and variations are intended to be included within thescope of this specification. As such, the claims may be amended torecite any features or characteristics expressly or inherently describedin, or otherwise expressly or inherently supported by, thisspecification. Further, Applicant(s) reserve the right to amend theclaims to affirmatively disclaim features or characteristics that may bepresent in the prior art. Therefore, any such amendments comply with therequirements of 35 U.S.C. §112, first paragraph, and 35 U.S.C. §132(a).The various embodiments disclosed and described in this specificationcan comprise, consist of, or consist essentially of the features andcharacteristics as variously described herein.

Any patent, publication, or other disclosure material identified hereinis incorporated by reference into this specification in its entiretyunless otherwise indicated, but only to the extent that the incorporatedmaterial does not conflict with existing description, definitions,statements, or other disclosure material expressly set forth in thisspecification. As such, and to the extent necessary, the expressdisclosure as set forth in this specification supersedes any conflictingmaterial incorporated by reference herein. Any material, or portionthereof, that is said to be incorporated by reference into thisspecification, but which conflicts with existing definitions,statements, or other disclosure material set forth herein, is onlyincorporated to the extent that no conflict arises between thatincorporated material and the existing disclosure material. Applicantsreserve the right to amend this specification to expressly recite anysubject matter, or portion thereof, incorporated by reference herein.

The grammatical articles “one”, “a”, “an”, and “the”, as used in thisspecification, are intended to include “at least one” or “one or more”,unless otherwise indicated. Thus, the articles are used in thisspecification to refer to one or more than one (i.e., to “at least one”)of the grammatical objects of the article. By way of example, “acomponent” means one or more components, and thus, possibly, more thanone component is contemplated and may be employed or used in animplementation of the described embodiments. Further, the use of asingular noun includes the plural, and the use of a plural noun includesthe singular, unless the context of the usage requires otherwise.

In rotary cutting and machining tools, a helical cutting edge graduallyengages a workpiece to the full length of the cutting edge, andgradually disengages from the workpiece as material is cut and removed.The cutting action from a helical cutting edge results in a smooth cutand evenly distributed stresses along the cutting edge. In contrast, astraight cutting edge engages a workpiece along the full length of thecutting edge at the same time. This abrupt engagement causes a rapidcutting tooth load, which may cause undesirable vibrations and tool“chatter.”

However, for cutting tools comprising indexable cutting inserts, if thearrangement of the multiple cutting inserts assembled and aligned on thetool holder does not form a continuous cutting edge having a truehelical geometric shape, the modular cutting tool may create a roughsurface finish and/or stepped/wavy surface topology on the machinedsurface. It is difficult to produce a cutting edge having a continuousand true helical geometric configuration on modular rotary cutting toolscomprising multiple cutting inserts because the length of the cuttingedge is formed by the respective cutting edges of the multipleindividual cutting inserts when assembled in the tool holder.

The uneven and rough surface topology of a cut made with a modularrotary cutting tool comprising a cutting flute comprising a series ofcutting inserts may be offset, in part, by another cutting flutecomprising another series of multiple cutting inserts. However, if thecutting edges of the flutes, which are formed by the cutting edges ofthe multiple individual cutting inserts comprising the cutting flutes,are not in a true helical form, the uneven and rough surface topologywill never be completely offset. This problem is even more pronouncedwith cutting inserts having sinusoidal or wavelike cutting edges becausethe non-linear and non-arcuate cutting edge pattern can createundulations in a machined surface, particularly when the individualcutting inserts are out of alignment.

Solid (i.e., unitary, one-piece) end mills having cutting edges havingsinusoidal or wavelike patterns from one end of the cutting portion tothe other along a perspective helical path may significantly improvecutting action and increase tool life in rotary milling applications.Examples of such solid end mills are described in U.S. Pat. Nos.4,212,568; 4,560,308; 5,610,232; 7,563,059; and 7,588,396, which areincorporated by reference herein. However, the unitary construction ofthese end mills facilitates the formation of true helical configurationsbecause there are no indexable or removal parts that create alignmentproblems, which prevent the formation of a helical cutting edge on amulti-insert cutting flute.

U.S. Pat. Nos. 5,221,164; 5,772,365; and 7,101,122 describe cuttinginserts having wavelike patterns on the individual inserts. However, theinserts described in these references are not structurally capable ofbeing assembled into a cutting flute positioned along and about thelength of a cutting tool holder. Therefore, these inserts cannot form atrue helical cutting edge. U.S. Pat. Nos. 6,773,209 and 6,811,359describe the problems encountered on machined surfaces caused by arotary milling operation using non-helical cutting tools. These patentsdescribe a helical cutting system comprising individual cutting insertshaving linear/arcuate cutting edges. However, these patents do notdefine the purported helical cutting edge mathematically orquantitatively and, therefore, do not enable the general design ofcutting flutes comprising indexable inserts and true helical cuttingedges.

As defined in Machinery's Handbook, 26th Edition, Industrial Press Inc.,New York, 2000 (which is incorporated by reference herein) a helix is acurve generated by a point moving about a cylindrical surface (real orimaginary) at a constant rate in the direction of the cylinder'slongitudinal axis. Therefore, geometrically, a helix is a spiral-shapedcurve in three-dimensional space. A helix has the property that atangent line at any point along the helix curve has a constant anglewith respect to a fixed line in space. When the fixed line is thecentral longitudinal axis of the helix, the constant angle is defined asthe “helix angle.” A helix may be defined parametrically in Cartesianand cylindrical coordinate systems as follows:

Cartesian coordinates Cylindrical coordinates x(t) = a cos(t); r(t) = ay(t) = a sin(t); θ(t) = t z(t) = bt h(t) = bt

In a right-handed Cartesian coordinate system, as the parameter tincreases, the point (x(t), y(t), z(t)) traces a right-handed helix ofradius a and pitch 2πb about the z-axis, which is parallel andcoincident (i.e., co-linear) with the longitudinal axis of the helix.The pitch of a helix is the length of one complete helix turn measuredparallel to the axis of the helix. Referring to FIG. 22, a cylindricalhelix is shown in which a=1 and b=1. The helix is shown with increasingparameter t from t=0 to t=4π (i.e., through two pitches of the helix).In a cylindrical coordinate system, as the parameter t increases, thepoint (r(t), θ(t), h(t)) traces a right-handed helix of radius a andpitch 2πb about the h-axis, which is co-linear with the longitudinalaxis of the helix.

As used herein, the terms “helix” and “helical” refer to cylindricalhelixes, i.e., helixes having a constant radius about a centrallongitudinal axis. A true helical cutting edge may be defined as athree-dimensional curved cutting edge in which each point on the cuttingedge is located at the same perpendicular distance to the centrallongitudinal axis of the rotary cutting tool (i.e., the cutting axis),within acceptable tolerances. This perpendicular distance is the cuttingradius of the rotary cutting tool, which is constant along the cuttinglength of the cutting tool. Therefore, each point on a helical cuttingedge is located on a conceptual cylindrical surface having a diameter oftwo times the cutting radius of the rotary cutting tool.

A helical cutting edge may be conceptually developed by moving a pointat a constant rate in the longitudinal direction of the cutting axis andat a constant circumferential rate, while maintaining a constantdistance (equal to the cutting radius) from the central longitudinalaxis (i.e., the cutting axis) of a cutting tool holder. A cutting edgedesigned in this manner is a true helical cutting edge and would notcreate uneven or rough machined surface topology, provided that thecutting edge maintains a true helical shape. This would result in asmooth and accurate cutting path in rotary machining applications, forexample. Further, combining a sinusoidal curve component with a helicalcurve component in a single cutting edge configuration would not preventsmooth and accurate cutting paths because each point of the cutting edgewould still coincide with the cutting radius.

The various non-limiting embodiments disclosed and described in thisspecification are directed, in part, to cutting inserts comprising atleast one sinusoidal and helical cutting edge, and to cutting toolsystems comprising the inserts, in which the assembly of the inserts ona tool holder forms a cutting flute comprising a sinusoidal and helicalcutting edge. As used herein, the term “sinusoidal and helical cuttingedge(s)” refers to the cutting edge portions of a cutting insert thatengage a workpiece and cut material from the workpiece, in which thecutting edges have a geometric shape comprising a sinusoidal curvecomponent and a helical curve component. As used herein, the term“sinusoidal and helical cutting edge(s)” also refers to the cutting edgeportions of a cutting flute comprising an assembly of cutting inserts,in which the cutting edges of the cutting flute have a geometric shapecomprising a sinusoidal curve component and a helical curve component.

Therefore, it is understood that the sinusoidal and helical cuttingedge(s) of a cutting flute are formed by the alignment of the sinusoidaland helical cutting edge(s) of individual cutting inserts helicallypositioned in a tool holder. In addition, it is understood that thesinusoidal and helical cutting edge(s) described in this specificationcomprise a combined sinusoidal and helical geometric shape withingenerally acceptable tolerances in the cutting tool industry.

The various non-limiting embodiments disclosed and described in thisspecification provide the advantage of improved cutting action andincreased tool life that result from sinusoidal cutting edges. Thevarious non-limiting embodiments disclosed and described in thisspecification also provide the advantage of improved surface finish andmore accurate machining path that result from true helical cuttingedges. Further, these advantages are provided in an indexable cuttingtool system in which individual cutting inserts may be indexed orreplaced as necessary due to wear or failure. Various non-limitingembodiments disclosed and described in this specification provide acutting tool system characterized by a combined sinusoidal and truehelical cutting edge, which improves the rotary machining ofdifficult-to-machine materials, such as, for example, titanium andtitanium alloys, nickel and nickel alloys, superalloys, and variousexotic metals and metallic composites.

The various embodiments disclosed and described in this specificationalso provide a design method for producing a cutting insert comprisingat least one indexable, sinusoidal, and helical cutting edge. Thisdesign method creates a mathematical design model that may be used tomanufacture cutting inserts having sinusoidal and helical cutting edgesthat together form a cutting flute having a sinusoidal and helicalcutting edge. The various embodiments disclosed and described in thisspecification also provide a design method for positioning multiplecutting inserts in a tool holder to form a cutting flute comprising acombined sinusoidal and helical cutting edge in a cutting tool system.This design method creates a design model that may be used to machinethe insert pockets on a tool holder so that indexable cutting insertsmay be assembled together and aligned to form a cutting flute comprisinga sinusoidal and helical cutting edge.

FIG. 1 is a three-dimensional perspective view of a cutting insert 10comprising two indexable cutting edges 15 and 16, each of the cuttingedges comprising a sinusoidal and helical cutting edge. The cuttinginsert 10 includes a center through-hole 11 for removably securing thecutting insert 10 to a tool holder (not shown). The sinusoidal andhelical cutting edge 15 is located on the top side 12 of the cuttinginsert 10. The cutting edge 15 comprises a one-wavelength sinusoidalshape. The cutting edge 15 comprises cutting edges 15 a and 15 b, whichare continuous with each other and each comprise a half-wavelengthsinusoidal shape. The cutting edge 15 comprises two optional nosecorners 15 c and 15 d located at the respective ends of the sinusoidaland helical cutting edge 15.

The cutting insert 10 also comprises a second cutting edge 16 located onthe bottom side 13 of the cutting insert. The cutting edge 16 comprisesa one-wavelength sinusoidal shape. The cutting edge 16 comprises cuttingedges 16 a and 16 b, which are continuous with each other and eachcomprise a half-wavelength sinusoidal shape. The cutting edge 16comprises two optional nose corners 16 c and 16 d located at therespective ends of the sinusoidal and helical cutting edge 16.

The nose corners 15 c/15 d and 16 c/16 d are formed from the initialsharp end points of the sinusoidal and helical cutting edges 15 and 16,respectively, in order to prevent the ends of the cutting edges of theinsert from being damaged during use in machining processes. The twosinusoidal and helical cutting edges 15 and 16 of the cutting insert 10are indexable by rotating the insert 180-degrees about an axisperpendicular to the axis of the center through-hole 11 and parallel tothe mean line of the sinusoidal curve component of the cutting edges 15and 16. This indexable feature is illustrated in FIGS. 2 and 3.

FIG. 2 is an end view of the cutting insert 10 shown in FIG. 1 (viewedfrom the end shown in perspective in FIG. 1). The plane 21 is a middleplane between the top face 12 and the bottom face 13 of the cuttinginsert 10. The plane 22 is perpendicular to the middle plane 21 andparallel and aligned with the central axis of the center through-hole11. The cutting insert 10 possesses 180-degree rotational symmetry aboutthe axis defined by the intersection of plane 21 and plane 22.Therefore, the top face 12 and the cutting edge 15 possesses 180-degreerotational symmetry with respect to the bottom face 13 and cutting edge16, and as such, the two sinusoidal and helical cutting edges 15 and 16of the cutting insert 10 are indexable by rotating the insert180-degrees about the axis defined by the intersection of plane 21 andplane 22.

FIG. 3 is a top view, together with two detailed views, of the cuttinginsert 10 shown in FIGS. 1 and 2 (viewed from the top face 12 shown inperspective in FIG. 1). The plane 22 is the same as the plane 22 shownin FIG. 2. As shown on the left-hand side of FIG. 3, the sinusoidal andhelical cutting edge 15 passes through the points P1, P2, and P3 (inwhich the points P1 and P3 are located at the ends of the cutting edgebefore the formation of the nose corner 15 d at the end point P3 of thecutting edge 15 b and the formation of the nose corner 15 c at the endpoint P1 of the cutting edge 15 a). As shown on the right-hand side ofFIG. 3, the sinusoidal and helical cutting edge 16 passes through thepoints P4, P5, and P6 (in which the points P4 and P6 are located at theends of the cutting edge before the formation of the nose corner 16 d atthe end point P6 of the cutting edge 16 b and the formation of the nosecorner 16 c at the end point P4 of the cutting edge 16 a.

The line 18 is the longitudinal axis of the sinusoidal curve defining,in part, the cutting edge 15 (i.e., the mean line of the sinusoidalcurve component), wherein the portion 15 a and the portion 15 b have thesame parameters (i.e., amplitude and wavelength). The line 19 is thelongitudinal axis of the sinusoidal curve defining, in part, the cuttingedge 16 (i.e., the mean line of the sinusoidal curve component), whereinthe portion 16 a and the portion 16 b have the same parameters (i.e.,amplitude and wavelength). Although the geometric parameters of portions15 a and 15 b of cutting edge 15 are the same as the geometricparameters of portions 16 a and 16 b, respectively, of cutting edge 15,it is understood that in various non-limiting embodiments, theseportions may not necessarily be the same.

FIG. 4 is a side view of the cutting insert 10 shown in FIGS. 1-3(viewed from the left side of the cutting insert as shown in FIG. 3).FIG. 4 illustrates the orientation of the sinusoidal and helical cuttingedges 15 and 16 relative to the middle plane 21 between the top face 12and the bottom face 13. The cutting edge 15 has a gradual downwardgradient from a high point (relative to middle plane 21) at the nosecorner 15 c on the cutting edge portion 15 a to a low point (relative tomiddle place 21) at the nose corner 15 d on the cutting edge portion 15b. The gradual downward gradient of the cutting edge 15 comprises thecombined geometric shape of a sinusoidal curve component and a truehelical curve component. Likewise, the cutting edge 16 has a gradualdownward gradient from a high point (relative to middle plane 21) at thenose corner 16 c on the cutting edge portion 16 a to a low point(relative to middle plane 21) at the nose corner 16 d on the cuttingedge portion 16 b. The gradual downward gradient of the cutting edge 16comprises the combined geometric shape of a sinusoidal curve componentand a true helical curve component.

FIG. 5(a) is a schematic end view and FIG. 5(b) is a schematic top viewof a cutting insert 50 illustrating the sinusoidal and helical cuttingedges 51 and 52 of the cutting insert. The cutting insert 50 shown inFIGS. 5(a) and 5(b) is generally the same as the cutting insert 10 shownin FIGS. 1-4 except that the cutting insert 50 does not have roundednose corners, but instead cutting insert 50 has points 56 at the ends ofthe sinusoidal and helical cutting edges 51 and 52 of the cuttinginsert. The points 56 are shown for the purpose of illustrating thegeometry of the sinusoidal and helical cutting edge 51 (on the top face53) and the sinusoidal and helical cutting edge 52 (on the bottom face54). The sinusoidal and helical cutting edge 51, for example, isconceptually produced by trimming a sinusoidal cutting edge to have acontour that coincides with a helical surface 55.

The helical surface 55 is geometrically defined to be coincident with atrue helix, as defined above, having a longitudinal axis 57. Thelongitudinal axis 57 of the helical surface 55 forms a helix angle Hawith the center plane 60 of the cutting insert 50. The helix angle Ha isthe same angle as the constant helix angle formed between a tangent lineat any point along the helix curve (defining the helix surface 55) andthe central longitudinal axis of the helix curve.

FIG. 6(a) is a top view schematic diagram, and FIGS. 6(b) and 6(c) areperspective view schematic diagrams, illustrating the geometricpositioning of the cutting insert 50 relative to a Cartesian coordinatesystem (XYZ), with the cutting insert positioned as if it were securedon a rotary tool holder (not shown). FIG. 6(b) is a perspective end viewof the insert 50 as oriented in FIG. 6(a) (i.e., as viewed along theY-coordinate direction as shown in FIG. 6(a)). FIG. 6(c) is aperspective side view of the insert 50 as oriented in FIG. 6(a) (i.e.,as viewed along the X-coordinate direction as shown in FIG. 6(a)).

The cutting insert 50 in FIG. 6(a) is shown in an orientation rotatedabout the origin O of the XOY plane of the XYZ coordinate system. Theangle of rotation of the insert 50 is equal to the helix angle Ha of thehelical surface 55, which defines the helical geometric component of thesinusoidal and helical cutting edge 51. In this manner, the cuttinginsert 50 is shown in an orientation as if the cutting insert werepositioned on a tool holder (not shown) having a cutting axis that isco-linear with the Y-axis of the XYZ coordinate system (see FIG. 21(a)).

The helical surface 55 is also rotated together with the cutting insertby the helix angle Ha (that is, the angle between the center plane 60 ofthe cutting insert 50 and the Y-axis of the XYZ coordinate system). Inthis manner, the angle formed between the center plane 60 of the cuttinginsert 50 and the longitudinal axis of the helix curve defining thehelical surface 50 (i.e., the helical geometric component of thesinusoidal and helical cutting edge 50) is set equal to the helix angleHa of the helix curve. As a result, the helical surface 55 is positionedcoincident with a conceptual cylindrical surface having a centrallongitudinal axis co-linear with the cutting axis of a tool holder (notshown) and having a cylindrical radius equal to the cutting radius R1 ofa cutting tool system comprising a tool holder and the cutting insert50. FIGS. 6(b) and 6(c) show the positioning of the cutting insert 50 inthe XOZ plane and the YOZ plane of the XYZ coordinate system,respectively, wherein the cutting edge 51 is located within the helicalsurface 55 having a helix radius of R1.

The formation of the sinusoidal and helical cutting edge 51 from P1 toP2 is, therefore, directly associated with the geometric relationshipbetween the cutting insert 50 and a tool holder (not shown). This isfurther illustrated in FIGS. 21(a) and 21(b). FIG. 21(a) is a schematicdiagram illustrating the positioning of a cutting insert 350 (comprisingtwo indexable, sinusoidal, and helical cutting edges) relative to a toolholder 300 and an XYZ coordinate system. The cutting insert 350 isgenerally identical to the cutting insert 50 shown in FIGS. 5 and 6. Thetool holder 300 has a central longitudinal cutting axis 310. The cuttinginsert 350 is positioned on the tool holder 300 so that the center plane360 of the cutting insert 350 forms an angle with the axis 310 that isequal to the helix angle Ha of the helical component of the sinusoidaland helical cutting edges of the cutting insert.

FIG. 21(b) is a schematic diagram illustrating the positioning of aseries of common cutting inserts 350, 350′, and 350″, each cuttinginsert comprising two indexable, sinusoidal, and helical cutting edges,relative to the tool holder 300 and the XYZ coordinate system. As usedherein, the term “common cutting inserts” and the like means insertshaving the same geometric configuration and dimensions to withingenerally acceptable tolerances in the cutting tool industry. Forinstance, in various non-limiting embodiments, the common cuttinginserts described in this specification may comprise a series (i.e., aplurality) of cutting inserts comprising the same material ofconstruction and having the same shape, cutting features, and dimensionsto within generally acceptable tolerances in the cutting tool industry.

The common cutting inserts 350, 350′, and 350″ are generally identicalto the cutting insert 50 shown in FIGS. 5 and 6, and together the seriesof common cutting inserts form a cutting flute comprising the cuttinginserts. The cutting flute comprises a cutting edge having a sinusoidaland helical geometric shape in which the sinusoidal and helical cuttingedge of the cutting flute is formed by the helical alignment of theindividual sinusoidal and helical cutting edges of the cutting insertson the tool holder. The center planes of the cutting inserts 350, 350′,and 350″ each form an angle Ha with the central longitudinal cuttingaxis 310 of the tool holder 300. The angle Ha formed between the centerplanes of the cutting inserts 350, 350′, and 350″ and the centrallongitudinal cutting axis 310 of the tool holder 300 is equal to thehelix angle of the helix 370. The helix 370 defines the helicalgeometric component of the sinusoidal and helical cutting edges of thecutting inserts and the combined sinusoidal and helical cutting edge ofthe cutting flute formed by the aligned cutting inserts.

Referring to FIG. 6, by geometrically defining the positioning of thecutting insert 50 relative to an XYZ coordinate system, positioned as ifthe cutting insert were mounted on a tool holder, a design method forproducing a cutting insert comprising at least one indexable,sinusoidal, and helical cutting edge may be used to create amathematical design model. The mathematical design model may be used tomanufacture cutting inserts having sinusoidal and helical cutting edgesthat together form a cutting flute comprising a sinusoidal and helicalcutting edge. The mathematical design model defines a cutting edgehaving a three-dimensional complex geometry comprising a combinedsinusoidal curve component and helical curve component. In accordancewith the mathematical model, every point along a sinusoidal and helicalcutting edge (e.g., cutting edges 51 and 52 in FIG. 6) is locatedprecisely on a conceptual cylindrical surface (e.g., surface 55 in FIG.6) defined by the cutting radius of a cutting tool system comprising atool holder (not shown in FIG. 6) and a plurality of common cuttinginserts (e.g., insert 50 in FIG. 6).

FIGS. 7(a), 7(b), and 7(c) are schematic diagrams illustrating curvesderived to establish a mathematical design model for the sinusoidal andhelical cutting edges of the insert shown in FIGS. 1-6, in which thecurves shown in FIGS. 7(a), 7(b), and 7(c) correspond to the cuttinginsert positioning shown in FIGS. 6(a), 6(b), and 6(c), respectively. Inorder to establish an equation for the sinusoidal and helical cuttingedge 51, two dashed-line sinusoidal curves 58 and 59 are introduced, asshown in FIG. 7(a). The two dashed-line curves 58 and 59 both have thesame geometric shape and dimensions as the cutting edge 51, but havedifferent orientations relative to the XYZ coordinate system. Thesinusoidal curve 58 has a mean line that is co-linear with the X-axis ofthe XYZ coordinate system. The sinusoidal curve 59 is parallel to thecutting edge 51 and centered on the origin O of the XYZ coordinatesystem. The cutting edge 51 may be regarded as a geometrictransformation of the curves 58 and 59, as shown in FIG. 7(a).

A mathematical equation may be established as follows for the curve 58according to the XOY plane of the XYZ coordinate system in FIG. 7(a),where the Y-axis is co-linear with the cutting axis of a cutting tool:

$\begin{matrix}{Y = {B \cdot {\sin( \frac{\pi}{A} )} \cdot X}} & (1)\end{matrix}$wherein the parameters B and A are defined in FIG. 7(a) as the amplitudeand half-wavelength of the sinusoidal component of the cutting edge 51.Equation (1) may be expressed in a general form as follows:f ₅₈(X,Y)=0  (2)Equation (2) generally defines the curve 58 as a function of the X and Yparameters of the XYZ coordinate system.

By introducing a rotation transformation (Ro), the following equationfor the curve 59 can be established from the rotation of the curve 58about the origin O in the XOY plane of the XYZ coordinate system:

$\begin{matrix}\begin{matrix}{{f_{59}( {X,Y} )} = {{f_{58}( {X,Y} )} \cdot {Ro}}} \\{= {{f_{58}( {X,Y} )} \cdot \begin{bmatrix}{\cos( {{90{^\circ}} - {Ha}} )} & {- {\sin( {{90{^\circ}} - {Ha}} )}} & 0 \\{\sin( {{90{^\circ}} - {Ha}} )} & {\cos( {{90{^\circ}} - {Ha}} )} & 0 \\0 & 0 & 1\end{bmatrix}}}\end{matrix} & (3)\end{matrix}$wherein Ha is the helix angle as shown in FIG. 6(a), FIG. 7(a), and FIG.21(a).

By introducing a translation transformation (Txy), the followingequation for the cutting edge 51 can be established from the translationof the curve 59 within the XOY plane:

$\begin{matrix}\begin{matrix}{{f_{51}( {X,Y} )} = {{f_{59}( {X,Y} )} \cdot {Txy}}} \\{= {{f_{59}( {X,Y} )} \cdot \begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\{{- G} \cdot {\cos({Ha})}} & {G \cdot {\sin({Ha})}} & 1\end{bmatrix}}}\end{matrix} & (4)\end{matrix}$wherein G is defined in FIG. 7(a) as the perpendicular distance betweenthe mean line of the cutting edge 51 and the mean line of the curve 59.Ha is the helix angle as described above.

As shown in FIG. 7(b), in the XOZ plane of the XYZ coordinate system,the cylindrical surface 55 is defined by the cutting radius R1 and theentire cutting edge is precisely located on the cylindrical surface 55.As discussed above, the cylindrical helix surface 55 shown in FIGS. 6and 7 is the same as the helical surface 55 shown in FIG. 5, but rotatedwith the cutting insert 50 by a helix angle Ha (relative to the XYZcoordinate system) so that the helical surface 55 becomes a cylindricalsurface 55 geometrically related to the cutting radius R1 of a cuttingtool comprising a tool holder and at least one cutting insert 50comprising a sinusoidal and helical cutting edge 51. Therefore, theequation of the cylindrical surface 55 in the XOZ plane, as shown inFIG. 7(b), may be expressed as:X ² +Z ² =R1²  (5)and in a general form as,f ₅₅(X,Z)=0  (6)wherein R1 is the radius of the circular cross-section of thecylindrical surface 55 in the XOZ plane, which is equal to the cuttingradius of a cutting tool with a cutting axis centered at the origin Oand perpendicular to XOZ plane of the XYZ coordinate system.

Referring to FIG. 7(b), where the cutting axis is represented by theY-axis (perpendicular to the plane of the page), and is centered at theorigin O, every point on the cutting edge 51 from P1 to P2 is located atthe cylindrical surface 55 defined by Equation (5). As noted above,every point on the cutting edge 51 from P1 to P2 is also located on thesinusoidal curve defined by Equation (4). By extending the sinusoidalcurve defined by Equation (4) (i.e., the sinusoidal component of thecutting edge 51) in the direction of +/−Z axis to become athree-dimensional sinusoidal surface perpendicular to the XOY plane, andby simultaneously extending the circular cross-section defined byEquation (6) (i.e., the helical component of the cutting edge 51) in thedirection of +/−Y axis to become a three-dimensional cylindrical surfaceperpendicular to the XOZ plane, two three-dimensional equations can beobtained.f ₅₁(X,Y,Z)=0  (7)f ₅₅(X,Y,Z)=0  (8)

An equation that mathematically defines the three-dimensional combinedsinusoidal and helical cutting edge 51, as shown in FIG. 6(c) and FIG.7(c) from P1 to P2, is obtained by solving Equations (7) and (8)simultaneously to obtain the equation of a three-dimensional curvedefining the intersection of the two above-described three-dimensionalsurfaces (i.e., the three-dimensional sinusoidal surface perpendicularto the XOY plane and the three-dimensional cylindrical surfaceperpendicular to the XOZ plane):

$\begin{matrix}{{f_{51}^{{3D} - C}( {X,Y,Z} )} = \{ \begin{matrix}{{f_{51}( {X,Y,Z} )} = 0} \\{{f_{55}( {X,Y,Z} )} = 0}\end{matrix} } & (9)\end{matrix}$where the superscript 3D-C indicates a three-dimensional curve.

The mathematical design method and resulting design models described inconnection with FIGS. 5-7 and Equations (1)-(9) may be used to designand fabricate cutting inserts having sinusoidal and helical cuttingedges. The mathematical design model defines a cutting edge having athree-dimensional complex geometry comprising a combined sinusoidalcurve component and helical curve component. The method may besummarized as follows.

First, conceptually positioning the cutting insert as if it were on atool holder and forming a helix angle relative to the longitudinal axisof the tool holder. Second, conceptually rotating the original helicalsurface (e.g., surface 55 in FIG. 5) by the same helix angle. Third,establishing a three-dimensional XYZ coordinate system with the Y-axisco-linear with the cutting axis of a cutting tool system defined by acutting radius that is centered at the cutting axis (e.g., radius R1 inFIGS. 6 and 7). Fourth, deriving equations that define the sinusoidaland helical components of the cutting edge relative to the coordinatesystem. In this manner, a helical surface (e.g., surface 55 in FIG. 5)is converted into a cylindrical surface (e.g., surface 55 in FIGS. 6 and7) that represents the cutting path defined by the cutting radius of thecutting tool system, and the sinusoidal surface intersected by thecylindrical surface mathematically defines a combined sinusoidal andhelical cutting edge.

The various embodiments disclosed and described in this specificationalso provide a design method for positioning multiple cutting inserts ona tool holder to form a cutting flute comprising a combined sinusoidaland helical cutting edge in a cutting tool system. This design methodcreates a design model that may be used to machine the insert pockets ina helical orientation on a tool holder so that indexable cutting insertsmay be assembled together and aligned to form a cutting flute comprisinga sinusoidal and helical cutting edge. This design method is also basedon the XYZ coordinate system established in connection with FIGS. 6-7,and may be used to specify the assembly of multiple cutting inserts onthe tool holder such that each cutting insert forms a portion of asinusoidal and helical cutting edge about the longitudinal cutting axis.

FIGS. 8(a) and 8(b) are schematic diagrams illustrating the relativepositioning of a series of common cutting inserts 50 and 62-66,positioned as if the cutting inserts were assembled and secured to arotary tool holder (not shown), and helically aligned to form a cuttingflute comprising the series of cutting inserts and having a cutting edgecomprising a sinusoidal and helical geometric shape. FIG. 8(a) is aschematic view from a direction perpendicular to the XOY plane of theXYZ coordinate system and FIG. 8(b) is a schematic view from a directionperpendicular to the XOZ plane of the XYZ coordinate system. In FIGS.8(a) and 8(b) the Y-axis is co-linear with the longitudinal cutting axisof the cutting tool system.

As shown in FIG. 8(b), the cylindrical surface 55 is defined by thecutting radius R1 located at the origin O. The cutting axis (i.e., theY-axis) is centered at the origin O and is perpendicular to the XOZplane. A first cutting insert 50 having two indexable sinusoidal andhelical cutting edges 51 and 52 is positioned in accordance with thedesign method described above. A series of common cutting inserts 62-66,which are geometrically and dimensionally the same as the cutting insert50, are positioned in helical alignment to form a cutting flute. Thesinusoidal and helical cutting edges of each insert comprising thecutting flute are in helical alignment and form a combined sinusoidaland helical cutting edge on the cutting flute.

In order to position the cutting inserts 62-66 to form a cutting flutecomprising a combined sinusoidal and helical cutting edge, the cuttinginserts may be positioned by: (1) rotating about the cutting axis (i.e.,the Y-axis) while maintaining the constant cutting radius R1; and (2)translating parallel to the cutting axis while maintaining the constantcutting radius R1. Any other positional changes for any of the multiplecommon cutting inserts 62-66 will cause the cutting inserts to bemisaligned and the cutting edges of the cutting inserts will not lie onthe cylindrical surface 55. Misalignment will create dimensional errorsin the actual cutting path of the cutting tool system (i.e., the cuttingpath will not be accurately and precisely defined by the cutting radiusR1). Misalignment will also alter the overall sinusoidal shape of thecutting edge and invalidate the overall helical shape of the cuttingflute, notwithstanding that each individual cutting insert has asinusoidal and helical cutting edge.

Geometrically, the position of each cutting insert 62-66 is initiallyset at the same position as the cutting insert 50 relative to the XYZcoordinate system, in which the cutting edge 51 is defined by Equation(9). The position of the cutting inserts 62-66 is then mathematicallyadjusted to an alignment position by rotating each insert about thecutting axis (i.e., the Y-axis) and translating each insert parallel tothe cutting axis while maintaining the constant cutting radius. Forexample, considering the cutting insert 62, which is positionedimmediately adjacent to the cutting insert 50 and has a cutting edge 72aligned with the cutting edge 51 of cutting insert 50, a first movementin the XYZ coordinate system is a three-dimensional rotationtransformation about the cutting axis (i.e., the Y-axis), and a secondmovement is a linear translation transformation parallel to the cuttingaxis. The translations from the position of cutting insert 50 to definethe position of cutting insert 72 are derived from Equation (9),defining the position of cutting insert 50, as follows:f ₇₂ ^(3D-C)(X,Y,Z)=f ₅₁ ^(3D-C)(X,Y,Z)·Ry(Q)·Txyz(J,K,L)  (10)wherein Ry represents a three-dimensional rotation matrix about theY-axis and Txyz represents a three-dimensional translation matrixparallel to the Y-axis, and the superscript 3D-C indicates athree-dimensional curve.

The rotation matrix and the translation matrix are defined as follows:

$\begin{matrix}{{{Ry}(Q)} = \begin{bmatrix}{\cos(Q)} & 0 & {\sin(Q)} & 0 \\0 & 1 & 0 & 0 \\{- {\sin(Q)}} & 0 & {\cos(Q)} & 0 \\0 & 0 & 0 & 1\end{bmatrix}} & (11) \\{{{Txyz}( {J,K,L} )} = \begin{bmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\J & K & L & 1\end{bmatrix}} & (12)\end{matrix}$wherein Q is the angle of rotation about the Y-axis, and J, K, and L arethe distances moved in each X, Y and Z direction, respectively. In orderto limit the linear movement of the translation transformation tomovement that is parallel to the Y-axis, J and L are set to zero.

The remaining cutting inserts 63-66 forming the cutting flute are thesame as the cutting insert 62. Therefore, a general equation formultiple common cutting inserts, such as, for example, cutting inserts62 to 66, may be expressed as indicated in Equation (13) below, assumingthe engaging cutting edge (i.e., the cutting edge in cutting action) ofthe first common cutting insert [f₁ ^(3D-C)(X,Y,Z)] is defined andpositioned in accordance with Equations (1) to (9) and the XYZcoordinate system established in FIGS. 6 to 8:f ₁ ^(3D-C)(X,Y,Z)=f ₁ ^(3D-C)(X,Y,Z)·Ry(i·Q)·Txyz(J,i·K,L)i=2, . . .,n  (13)wherein i represents the engaging cutting edge for the ith commoncutting insert among a total of n cutting inserts, and f₁ ^(3D-C)(X,Y,Z)represents the position of the engaging cutting edge of the ith commoncutting insert in the XYZ coordinate system.

In this manner, the position of each sinusoidal and helical cuttinginsert on a tool holder with a defined cutting diameter (or radius) ismathematically defined so that the overall cutting edge of the cuttingflute formed from the assembly and alignment of the individual commoncutting inserts is a combined sinusoidal and helical cutting edge, asshown in FIG. 8.

The mathematical design method and resulting design models described inconnection with FIG. 8 and Equations (10)-(13) may be used tomanufacture cutting tool holders having insert pockets configured tomechanically engage and secure a series of cutting inserts havingsinusoidal and helical cutting edges so that the secured inserts arehelically aligned to form a cutting flute on the tool holder andcomprising a sinusoidal and helical cutting edge. The mathematicaldesign model defines the positioning of the series of cutting inserts sothat the cutting edge of the cutting flute has a three-dimensionalcomplex geometry comprising a combined sinusoidal curve component andhelical curve component.

The design methods and models described in this specification fordefining and positioning multiple cutting inserts on a tool holder arefundamentally different than and distinct from prior design methods thatdepend on multiple discrete positional parameters such as, for example,cutting diameter (or radius), axial angle, radial angle, and the like.It is not possible to specify with mathematical accuracy and precision acomplex three-dimensional sinusoidal and helical cutting edge comprisingmultiple cutting inserts using prior design methods.

In various non-limiting embodiments, a method for designing and/orproducing a sinusoidal and helical cutting edge on a cutting insertcomprises:

(a) positioning a cutting insert having a sinusoidal-shaped cutting edgeas if it were on a tool holder with a helix angle; and

(b) modifying the sinusoidal shape of the cutting edge of the cuffinginsert to coincide with a cylindrical surface defined by the cuttingradius centered at the cutting axis of a cutting tool system.

In various non-limiting embodiments, a method for designing and/orproducing an assembly of common cutting inserts forming a cutting flutecomprising a sinusoidal and helical cutting edge (wherein each cuttinginsert comprises at least one sinusoidal and helical cutting edge)comprises:

(a) placing a first cutting insert at the position where its cuttingedge is defined in accordance with the above-described method fordesigning the sinusoidal and helical cutting edge;

(b) rotating a second cutting insert (and each subsequent cutting insertthereafter) about the cutting axis of a cutting tool system; and

(c) translating the second cutting insert (and each subsequent cuttinginsert thereafter) parallel to the cutting axis.

In various non-limiting embodiments, a method for designing multipleinsert pockets to secure multiple common cutting inserts forming acutting flute comprising a sinusoidal and helical cutting edge on acutting tool holder of a cutting tool system comprises:

(a) positioning a seating surface of the first insert pocket accordingto the assembly position of the first common cutting insert having asinusoidal-shaped cutting edge as if it were on a tool holder with ahelix angle;

(b) rotating the seating surface of a second insert pocket (and eachsubsequent insert pocket thereafter) about the cutting axis of a cuttingtool system; and

(c) translating the seating surface of the second insert pocket (andeach subsequent insert pocket thereafter) parallel to the cutting axiswhile maintaining a constant cutting radius as defined by the cuttingtool system.

In various non-limiting embodiments, a cutting insert may bemanufactured based on a design model developed using a method fordefining the sinusoidal and helical cutting edge. In variousnon-limiting embodiments, a tool holder configured to engage, secure,and align multiple cutting inserts in multiple respective insert pocketsmay be manufactured based on the design model developed in the methodfor defining the positioning of cutting inserts forming a cutting flutecomprising a sinusoidal and helical cutting edge (wherein each cuttinginsert comprises at least one sinusoidal and helical cutting edge). Forexample, cutting inserts comprising at least one sinusoidal and helicalcutting edge may be fabricated using automated grinding techniques basedon the design model described above in connection with Equations(1)-(9), and tool holders may be fabricated using computer numericalcontrol (CNC) machining based on the assembly design model describedabove in connection with Equations (10)-(13).

The cutting inserts manufactured based on the first design method may beassembled on a tool holder manufactured based in the second designmethod to form a cutting tool system. In various non-limitingembodiments, the cutting tool system may comprise a tool holdercomprising a plurality of common insert pockets positioned in a helicalorientation about a longitudinal axis of the tool holder. As usedherein, the term “common insert pockets” and the like means a commoncutting insert can be secured into any common insert pocket even thoughsome of the common insert pockets may be different in geometry. Inparticular, the common insert pocket adjacent to the insert pocket of anend-face cutting insert and the last common insert pocket at theproximal of a cutting flute (proximal relative to a shank portion of acutting tool holder comprising the cutting flute) may have differentgeometry but nonetheless be common insert pockets because a commoncutting insert is securable in the respective common insert pockets. Thecutting tool system may also comprise a plurality of common cuttinginserts removably attachable to the plurality of common insert pocketsin the tool holder to form at least one cutting flute on the toolholder, the at least one cutting flute comprising a helical grouping ofcommon cutting inserts positioned in the insert pockets. The commoncutting inserts each comprise at least one sinusoidal and helicalcutting edge. The at least one cutting flute comprises a sinusoidal andhelical cutting edge positioned about the longitudinal axis of the toolholder and formed by alignment of the individual sinusoidal and helicalcutting edges of the common cutting insert that comprise the at leastone cutting flute.

In various rotary machining applications using cutting tools comprisingmultiple indexable cutting inserts, a special front end-face cuttinginsert may be advantageous. As used herein, the term “end-face cuttinginsert” refers to a cutting insert configured to be positioned at thefront face end of a tool holder to axially engage a workpiece surface ina direction parallel to the longitudinal axis of the tool holder. Invarious non-limiting embodiments, an end-face cutting insert engages aworkpiece surface both axially and circumferentially, for example, ifthe end-face cutting insert is positioned at the periphery of a frontend face of a tool holder. In various non-limiting embodiments, acutting tool system comprises an end-face cutting insert configured toat least axially engage a workpiece during machining operations whenassembled on a tool holder.

FIGS. 9(a)-9(c) show an end-face cutting insert 80 having two indexablecutting edges (85 and 86). The end-face cutting insert 80 is configuredto be used as a different end-face cutting insert in combination withthe common cutting inserts shown in FIG. 8 in a cutting tool systemcomprising sinusoidal and helical cutting edges.

As shown in FIG. 9(a), the end-face cutting insert 80 comprises a centerthrough-hole 81 (configured to secure the cutting insert to a toolholder) and two identical cutting edges 85 and 86. The cutting edges 85and 86 are located on the top side 82 and the bottom side 83,respectively. The cutting edges 85 and 86 are helical-shaped cuttingedges. The two ends of the cutting edge 85 are rounded with nose corners85 a and 85 b. The two ends of the cutting edge 86 are also rounded withnose corners. The end-face cutting insert 80 is positioned with cuttingedge 85 forming an angle with a cutting axis 84 equal to the helix angleHa of the helix curve defining the helical shape of the cutting edge 85.

FIGS. 10(a) and 10(b) are schematic diagrams illustrating the relativepositioning of a series of common cutting inserts 90-97 and an end-facecutting insert 80, positioned as if the cutting inserts were assembledand secured to a rotary tool holder (not shown) to form a cutting flutecomprising the series of cutting inserts and comprising a sinusoidal andhelical cutting edge. The engaging cutting edge 100 of the commoncutting insert 90 is defined and positioned in accordance with Equation(9), and the engaging cutting edges 101-107 of the common cuttinginserts 91-97, respectively, are positioned in accordance with Equation(13).

The end-face cutting insert 80 is positioned in accordance with Equation(13) with i=2, but using a different rotating angle Q and a differenttranslating distance value K because the cutting edge 85 of the end-facecutting insert 80 is different than the cutting edges 100-107 of thecommon cutting inserts 90-97. The cutting edges 100-107 of the commoncutting inserts 90-97 form a combined sinusoidal and helical cuttingedge in the direction of and about the longitudinal axis of the toolholder (not shown) (i.e., the Y axis). As shown in FIG. 10(b), all ofthe cutting edges 100-107 of the common cutting inserts 90-97, and thecutting edge 85 of the end-face cutting insert 80, are precisely andaccurately located on the cylindrical surface 99 representing thecutting diameter/radius of a rotary cutting tool system.

FIGS. 11(a) and 11(b) are schematic diagrams illustrating the relativepositioning of a series of different-sized end-face cutting inserts 80,111, 112, 113, and 114, positioned as if the end-face cutting insertswhere assembled and secured to a rotary tool holder (not shown)configured to comprise five cutting flutes. In order to offset any gapbetween two adjacent cutting inserts in a cutting flute comprising thecutting inserts (e.g., gaps between adjacent common cutting inserts orgaps between an end-face cutting insert and an adjacent common cuttinginsert), it may be advantageous to make multiple end-face cuttinginserts, each end-face cutting insert having a different length on thecutting edge. For example, as shown in FIG. 11(a), the multiple end-facecutting inserts 80 and 111-114 each have a different length L1-L5,respectively.

As shown in FIG. 11(b), each end-face cutting insert has at least one,and in various non-limiting embodiments, two indexable cutting edges,that is, cutting edges 85 and 86 of the end-face cutting insert 80,cutting edges 121 and 122 of the end-face cutting insert 111, cuttingedges 123 and 124 of the end-face cutting insert 112, cutting edges 125and 126 of the end-face cutting insert 113, and cutting edges 127 and128 of the end-face cutting insert 114. All of the workpiece-engagingcutting edges (i.e., cutting edges 85, 121, 123, 125, and 127 of thecutting inserts 80 and 111-114, respectively) are located on thecylindrical surface 118 representing the cutting diameter/radius of arotary cutting tool system.

FIGS. 12(a) and 12(b) are schematic diagrams illustrating the relativepositioning of five (5) cutting flutes, each flute comprising adifferent-sized end-face cutting insert (80, 111-114), and a series ofcommon cutting inserts, positioned as if the cutting inserts wereassembled and secured to a rotary tool holder (not shown). The five (5)cutting flutes each comprise a sinusoidal and helical cutting edgeformed by the assembly and alignment of the sinusoidal and helicalcutting edges of the common cutting inserts. The end-face cuttinginserts (e.g., insert 80) are positioned and helically aligned withadjacent common cutting inserts (e.g., insert 90).

The position of each cutting insert is defined in accordance withEquation (13), wherein each end-face cutting insert (80, 111-114) mayhave a set of different values for the Q and K parameters. All engagingcutting edges, including the helical cutting edges of the end-facecutting inserts 80 and 111-114, are located on the cylindrical surface138 representing the cutting diameter/radius of a rotary cutting toolsystem. In various non-limiting embodiments, it may be advantageous tooverlap the cutting edges in the direction of the longitudinal cuttingaxis between the inserts comprising adjacent cutting flutes. Overlappingcutting edges may improve cutting accuracy and precision becausetrailing cutting flutes will remove uncut material left by the cuttingaction performed by leading cutting flutes. In this manner, a pluralityof cutting flutes, each flute comprising a helically aligned assembly oflongitudinally offset common cutting inserts, results in a fullyeffective cutting flute.

The amount of residual material left by the cutting action of a leadingcutting flute may be related to the degree of nose corner rounding ofthe cutting inserts of the cutting flute. In various non-limitingembodiments, sinusoidal and helical cutting inserts comprising roundednose corners may form small gaps in the combined sinusoidal and helicalcutting edge of the cutting flute comprising the cutting inserts. Atrailing cutting flute comprising a helically aligned assembly of commoncutting inserts that are longitudinally offset relative to the insertsthat comprise a leading cutting flute will cut and/or remove anyresidual material because the rounded nose corners of the insertscomprising the trailing cutting flute are longitudinally off-setrelative to the nose corners of the inserts comprising the leadingcutting flute. In other words, the junctions between the constituentcutting inserts of the cutting flutes are not aligned in a planeperpendicular to the longitudinal cutting axis of a rotary cutting tool.

A plurality of cutting flutes, each flute comprising an aligned assemblyof off-set common cutting inserts, is shown in FIG. 12(b). In variousnon-limiting embodiments, residual material left by a leading cuttingflute may be cut and/or removed by a trailing cutting flute because ofthe off-set established by end-face cutting inserts that have differentshapes and/or dimensions. For example, end-face cutting inserts 80 and111-114 in FIGS. 11 and 12 are commonly-shaped anddifferently-dimensioned (i.e., having different lengths L1-L5 as shownin FIG. 11(a)). The different length cutting edges of the end-facecutting inserts 80 and 111-114 effectively off-set the junctions (and,therefore, any gaps due to rounded nose corners, or in some cases due tothe geometric constraints of cutting inserts) between adjacent cuttinginserts comprising the cutting flutes.

In various non-limiting embodiments, it may be desirable for the cuttinginserts comprising each respective cutting flute to completely overlap(i.e., not be longitudinally off-set) between each adjacent cuttingflute. In other words, the junctions between the constituent cuttinginserts of the cutting flutes are aligned in a plane perpendicular tothe longitudinal cutting axis of a rotary cutting tool system. Byadjusting the values of the Q and K parameters in Equation (13), anarrangement of the assembly of common cutting inserts and, optionally,the end-face cutting inserts, may be defined for a rotary cutting toolsystem comprising at least one cutting flute comprising at least oneassembly of common cutting inserts, wherein the individual inserts andthe cutting flute comprise sinusoidal and helical cutting edges.

FIGS. 13(a) and 13(b) show two views of a cutting tool system 140comprising a tool holder 146 and five cutting flutes 141-145, eachcutting flute comprising a different-sized end-face cutting insert(e.g., cutting insert 147 a) and a series of common cutting inserts(e.g., cutting insert 147 b), and each cutting flute 141-145 alsocomprising a sinusoidal and helical cutting edge. The tool holder 146comprises five series of common insert pockets (e.g., insert pocket148), each series of common insert pockets positioned in a helicalorientation about a longitudinal axis of the tool holder 146. Aplurality of common cutting inserts are removably attachable to thecommon insert pockets in the tool holder 146 to form five cutting flutes141-145 on the tool holder. In some embodiments, the insert pockets forthe first common cutting insert (e.g., cutting insert 147 c) and thelast common cutting insert (e.g., cutting insert 147 d) may be slightlydifferent in geometry from the rest due to the fact that the firstinsert pocket for a first common cutting insert adjoins the insertpocket for an end-face cutting insert and the last insert pocket for alast common cutting insert ends at the proximal end of the flute. Thefive cutting flutes each comprise a helical grouping of the commoncutting inserts positioned in the insert pockets. The common cuttinginserts each comprise at least one sinusoidal and helical cutting edge.The five cutting flutes 141-145 each comprise a sinusoidal and helicalcutting edge positioned about the longitudinal axis of the tool holder146 and formed by the alignment of the individual sinusoidal and helicalcutting edges of the common cutting inserts that comprise the fivecutting flutes.

The five cutting flutes 141-145 shown in FIG. 13(b) each comprise adifferent-sized end-face cutting insert having at least one indexablehelical cutting edge. The five cutting flutes 141-145 also comprisemultiple common cutting inserts, the cutting inserts having sinusoidaland helical cutting edges that are aligned to form the sinusoidal andhelical cutting edges of the cutting flutes. As shown in FIG. 13(a), theworkpiece-engaging cutting edges of the cutting inserts (and, therefore,the cutting edges of the cutting flutes) are located on the cylindricalsurface 149 representing the cutting diameter/radius of the cutting toolsystem. As shown in FIG. 13(b), the five different-sized end-facecutting inserts have a common longitudinal clearance, i.e., extendbeyond the end face of the tool holder 146 by the same distance in thedirection parallel to the longitudinal axis of the tool holder.

FIGS. 14(a)-14(c) show three views of a cutting insert 150 comprisingfour indexable cutting edges 151-154, each cutting edge comprising asinusoidal and helical geometric shape. The cutting insert 150 comprisesa center through-hole 155 for mounting and securing the cutting insertto a tool holder (not shown). The cutting insert 150 also comprises atop side 156 and a bottom side 157. The four indexable, sinusoidal, andhelical cutting edges 151-154 are located on the top side 156 of thecutting insert 150. The cutting insert 150 possesses 90-degreerotational symmetry about the central axis of the through-hole 155.

The four sinusoidal and helical cutting edges 151-154 of the cuttinginsert 150 are indexable by rotating the insert 90-degrees about thecentral axis of the through-hole 155. As shown in FIG. 14(b), thecutting edge 151 from point N1 through N2 to N3 is a one-wavelengthsinusoidal curve, wherein line 158 is the longitudinal mean line axis ofthe sinusoidal curve, and the line 159 is the vertical axis of thesinusoidal curve. In some embodiments, the existing sinusoidal cuttingedge 151 shown in FIG. 14 may be in an alternative shape being mirroredvia the longitudinal mean line 158, that is, a sinusoidal cutting edgewith its sole peak point positioned along the vertical line 159 butabove the longitudinal line 158 of sinusoidal the curve.

FIGS. 15(a)-15(c) are schematic diagrams illustrating the geometricpositioning of the cutting insert 150 relative to an XYZ coordinatesystem as if the cutting insert were secured to a rotary tool holder(not shown). FIG. 15(a) is a side view schematic diagram of the cuttinginsert 150 as positioned on the tool holder with the longitudinal axis164 of the sinusoidal cutting edge 151 forming a helix angle Ha with thelongitudinal cutting axis 163 of a cutting tool system, which isco-linear with the Y-axis of the XYZ coordinate system. FIG. 15(c) is aperspective view schematic diagram of the cutting insert 150 as viewedalong the direction of the Y-axis (i.e., along the cutting axis 163) asshown in FIG. 15(a). FIG. 15(c) illustrates that the entire sinusoidaland helical cutting edge 151 is located on the cylindrical surface 166defined by the cutting radius R4, wherein the cutting axis 163 iscentered at the origin O in FIG. 15(c). Therefore, the sinusoidal andhelical cutting edges 151-154 of the cutting insert 150 produce anaccurate cutting path defined by the cutting radius R4 centered at thecutting axis 163. The design model and equations that define thesinusoidal and helical cutting edges 151-154 of the cutting insert 150are developed using the same design method described above in connectionwith Equations (1)-(9).

FIGS. 16(a) and 16(b) are schematic diagrams illustrating the relativepositioning of a series of common cutting inserts 150 and 171-175,positioned as if the cutting inserts were assembled and secured to arotary tool holder (not shown) to form a cutting flute 170 comprisingthe series of common cutting inserts and comprising a sinusoidal andhelical cutting edge formed by the aligned sinusoidal and helicalcutting edges of the series of common cutting inserts. The commoncutting inserts 150 and 171-175 each comprise four indexable,sinusoidal, and helical cutting edges (e.g., cutting edges 151 and181-185 on cutting inserts 150 and 171-175, respectively). Although adifferent end-face cutting insert is not shown in FIG. 16, it isunderstood that the embodiment illustrated in FIG. 16 may furthercomprise a different end-face cutting insert. The design model andequations that define the positioning of the cutting inserts 150 and171-175 to form a cutting flute comprising a sinusoidal and helicalcutting edge formed by the indexable, sinusoidal, and helical cuttingedges 151 and 181-185 (including the positioning of a different end-facecutting insert, not shown) are developed using the same design methoddescribed above in connection with Equations (10)-(13).

The longitudinal cutting axis 177 of the rotary cutting tool systemcomprising the cutting inserts 150 and 171-175 is co-linear with theY-axis of the XYZ coordinate system. The sinusoidal and helical cuttingedge of the cutting flute 170 formed from the aligned cutting edges 151and 181-185 of the individual cutting inserts 150 and 171-175,respectively, includes gaps between the adjacent cutting inserts thatcomprise the cutting flute. For example, a gap labeled Ygap in FIG.16(a) is shown between the cutting edges 182 and 183 of cutting inserts172 and 173, respectively, of the cutting flute 170. As shown in FIG.16(b), notwithstanding the gap between adjacent cutting inserts, theworkpiece-engaging cutting edges 151 and 181-185, which form thesinusoidal and helical cutting edge of the cutting flute 170, arelocated on the cylindrical surface 178 defined by a cutting radius R4centered at the origin O, wherein the cutting axis 177 is also centeredat the origin O.

The gap between the adjacent cutting inserts of a cutting flute may becompensated for by longitudinally offsetting the cutting insertsrelative to adjacent cutting flutes, as described above. For example, atrailing cutting flute comprising an assembly of common cutting insertsmay be longitudinally offset along the Y-axis relative to a leadingcutting flute. In other words, the gaps between the constituent cuttinginserts of the cutting flutes are not aligned in a plane perpendicularto the longitudinal cutting axis of a rotary cutting tool systemcomprising the cutting flutes.

FIGS. 17(a) and 17(b) are schematic diagrams illustrating the relativepositioning of a common cutting insert 191 having two indexable cuttingedges 195 and 196, and a different end-face cutting insert 192 havingtwo indexable cutting edges 197 and 198, positioned as if the cuttinginserts were assembled and secured to a rotary tool holder (not shown)to form a cutting flute 190 comprising the cutting inserts and alsoforming a cutting edge having a sinusoidal and helical geometric shape.The cutting edges 195-198 are sinusoidal and helical cutting edges. Theworkpiece-engaging cutting edge 195 of the common cutting insert 190 isdefined and positioned using a design model derived using the designmethod described above in connection with Equations (1)-(9). The cuttinginserts are positioned to form a cutting flute comprising a sinusoidaland helical cutting edge using a design model derived using the designmethod described above in connection with Equations (10)-(13). As shownin FIG. 17(a), the work-piece engaging cutting edges 197 and 195, whichform the sinusoidal and helical cutting edge of the cutting flute 190,are located on the cylindrical surface 194 defined by a cutting radiusR2 centered at the origin O, wherein the longitudinal cutting axis 193is also centered at the origin O.

FIGS. 18(a) and 18(b) are two views of a cutting insert 200 comprisingtwo indexable cutting edges 201 and 202, each cutting edge having asinusoidal and helical geometric shape. The cutting insert 200 comprisestwo through-holes 204 and 205 for securing the cutting insert to a toolholder (not shown). As shown in FIG. 18(b), the cutting edge 201 frompoint G1 through G2 to G3 comprises a one-wavelength sinusoidal curve inwhich line 206 is the longitudinal mean line axis of the sinusoidalcurve, and the line 207 is the vertical axis of the sinusoidal curve. Asshown in FIG. 18(a), the sinusoidal curve passing through points G1, G2,and G3 follows a helical surface 208 on the top side 209 of the cuttinginsert 200.

FIGS. 19(a) and 19(b) show two views of a cutting insert 210 comprisingtwo indexable cutting edges 211 and 212, each cutting edge having asinusoidal and helical shape. The cutting insert 210 comprises a centerthrough-hole 215 for securing the cutting insert to a tool holder (notshown). As shown in FIG. 19(b), the cutting edge 210 from point H1through H2 to H3 comprises a one-wavelength sinusoidal curve in whichline 216 is the longitudinal mean line axis of the sinusoidal curve, andthe line 217 is the vertical axis of the sinusoidal curve. As shown inFIG. 19(a), the sinusoidal curve passing through points H1, H2, and H3follows a helical surface 218 on the top side 219 of the cutting insert210.

FIG. 20 is a three-dimensional perspective view of a cutting insert 220(similar to the cutting insert shown in FIGS. 1-6 and 8) comprising twoindexable, sinusoidal, and helical cutting edges 221 and 22, and furthercomprising notches 227 and 228 positioned along the cutting edges 221and 222, respectively. The cutting insert 220 comprises a centerthrough-hole 225 for securing the insert to a tool holder (not shown).The cutting edge 221 is located on the top side 223 of the cuttinginsert 220 and comprises cutting edges 221 a and 221 b, and nose corners221 c and 221 d. The cutting edge 222 is located on the bottom side 224of the cutting insert 220 and comprises cutting edges 222 a and 222 b,and nose corners 222 c and 222 d.

The nose corners 221 c/221 d and 222 c/222 d are formed from the initialsharp end points of the sinusoidal and helical cutting edges 221 and222, respectively, in order to prevent the ends of the cutting edges ofthe cutting insert from being damaged during use in machining processes.The two sinusoidal and helical cutting edges 221 and 222 of the cuttinginsert 220 are indexable by rotating the insert 180-degrees about anaxis perpendicular to the axis of the center through-hole 225 andparallel to the mean line of the sinusoidal curves of the cutting edges221 and 222.

The notches 227 positioned along the cutting edge 221, and the notches228 positioned along the cutting edge 222, may be in any geometric formor shape. In various non-limiting embodiments, the number of notchespositioned in a cutting edge may be at least one, and in someembodiments, may range from 1 to 10 per cutting edge. In variousnon-limiting embodiments, notches may be uniformly distributed along acutting edge or non-uniformly distributed along a cutting edge.

In various non-limiting embodiments, a cutting tool system comprises atool holder and a plurality of common cutting inserts. The tool holdercomprises a plurality of common insert pockets positioned in a helicalorientation about a longitudinal axis of the tool holder. The pluralityof common cutting inserts are removably attachable to the plurality ofcommon insert pockets in the tool holder. When so attached, theplurality of common cutting inserts form at least one cutting flute onthe tool holder. The at least one cutting flute comprises a helicalgrouping of common cutting inserts positioned in the insert pockets. Thecommon cutting inserts each comprise at least one sinusoidal and helicalcutting edge. The at least one cutting flute comprises a sinusoidal andhelical cutting edge positioned about the longitudinal axis of the toolholder. The sinusoidal and helical cutting edge of the cutting flute isformed by alignment of the individual sinusoidal and helical cuttingedges of the common cutting inserts that comprise the at least onecutting flute.

In various non-limiting embodiments, a cutting tool system comprises atool holder and a plurality of common cutting inserts. The tool holdercomprises two or more series of common insert pockets. Each series ofcommon insert pockets are positioned in a helical orientation about alongitudinal axis of the tool holder. The plurality of common cuttinginserts are removably attachable to the common insert pockets in thetool holder. When so attached, the plurality of common cutting insertsform two or more cutting flutes on the tool holder. The two or morecutting flutes each comprise a helical grouping of the common cuttinginserts positioned in the insert pockets. The common cutting insertseach comprise at least one sinusoidal and helical cutting edge. The twoor more cutting flutes each comprise a sinusoidal and helical cuttingedge positioned about the longitudinal axis of the tool holder. Thesinusoidal and helical cutting edge of the cutting flute is formed byalignment of the individual sinusoidal and helical cutting edges of thecommon cutting inserts that comprise the two or more cutting flutes.

In various non-limiting embodiments, at least one sinusoidal and helicalcutting edge of a common cutting insert may comprise a shape of onesinusoidal wavelength. In various non-limiting embodiments, a cuttinginsert may comprise two or more sinusoidal and helical cutting edgesthat are indexable in insert pockets in a tool holder, such as, forexample, comprising two sinusoidal and helical cutting edges or four (4)sinusoidal and helical cutting edges that are indexable in the insertpockets.

In various non-limiting embodiments, a cutting tool system may alsocomprise an end-face cutting insert removably attachable to an insertpocket positioned at an engaging end of a tool holder, the end-facecutting insert having a shape that is different than a shape of aplurality of common cutting inserts. In various non-limitingembodiments, an end-face cutting insert may comprise a helical cuttingedge that helically aligns with the sinusoidal and helical cutting edgesof a plurality of common cutting inserts that form the sinusoidal andhelical cutting edge of at least one cutting flute. In variousnon-limiting embodiments, an end-face cutting insert may comprise asinusoidal and helical cutting edge that helically aligns with thesinusoidal and helical cutting edges of a plurality of common cuttinginserts that form the sinusoidal and helical cutting edge of at leastone cutting flute.

In various non-limiting embodiments, a cutting tool system may compriseadjacent helical groupings of common cutting inserts that are offsetrelative to each other along the longitudinal axis of a tool holder sothat the inserts comprising adjacent helical cutting flutes are notlongitudinally aligned in a cross sectional plane perpendicular to thelongitudinal axis. In various non-limiting embodiments, a cutting toolsystem may comprise two or more differently-sized end-face cuttinginserts that are positioned in respective insert pockets with a commonlongitudinal clearance, so that adjacent helical groupings of the commoncutting inserts are offset relative to each other along the longitudinalaxis of the tool holder so that the inserts comprising adjacent helicalflutes are not longitudinally aligned in a cross sectional planeperpendicular to the longitudinal axis.

The non-limiting embodiments described in this specification aredirected to cutting inserts and cutting tool systems comprisingsinusoidal and helical cutting edges. The embodiments described in thisspecification provide various advantages including, for example,improved cutting action and increased tool life as a result ofsinusoidal cutting edge geometry, and improved machined surface finishand machining path accuracy as a result of helical cutting edgegeometry. The cutting inserts described herein comprising a sinusoidaland helical cutting edge may be manufactured in various sizes andshapes, and configured for use in a variety of rotary machiningapplications. It is understood that cutting inserts produced inaccordance with the embodiments described herein may include acceptablemanufacturing tolerances in terms of size, shape, and other geometricparameters.

This specification has been written with reference to variousnon-limiting and non-exhaustive embodiments. However, it will berecognized by persons having ordinary skill in the art that varioussubstitutions, modifications, or combinations of any of the disclosedembodiments (or portions thereof) may be made within the scope of thisspecification. For instance, the cutting tool system disclosed in thisspecification comprising a plurality of common cutting inserts formingat least one sinusoidal and helical cutting edge may be designed to havedifferential helix, differential pitch or non equi-spaced cuttingflutes, and the cutting inserts presented in this invention may havenon-standard sinusoidal wave patterns, and correspondingly, there may bea second group of common cutting inserts that are different in geometryfrom the first group of common cutting inserts. Thus, it is contemplatedand understood that this specification supports additional embodimentsnot expressly set forth herein. Such embodiments may be obtained, forexample, by combining, modifying, or reorganizing any of the disclosedsteps, components, elements, features, aspects, characteristics,limitations, and the like, of the various non-limiting embodimentsdescribed in this specification. In this manner, Applicants reserve theright to amend the claims during prosecution to add features asvariously described in this specification, and such amendments complywith the requirements of 35 U.S.C. §112, first paragraph, and 35 U.S.C.§132(a).

What is claimed is:
 1. A cutting tool system comprising: a tool holdercomprising a plurality of common insert pockets positioned in a helicalorientation about a longitudinal axis of the tool holder; and aplurality of common cutting inserts removably attachable to theplurality of common insert pockets in the tool holder to form at leastone cutting flute on the tool holder, the at least one cutting flutecomprising a helical grouping of common cutting inserts positioned inthe insert pockets; wherein the common cutting inserts each comprise atleast one sinusoidal and helical cutting edge; wherein two or more ofthe cutting inserts combine to define a sinusoidal wavelength shapedefined by one period per cutting insert; and wherein the at least onecutting flute comprises a sinusoidal and helical cutting edge positionedabout the longitudinal axis of the tool holder and formed by alignmentof the individual sinusoidal and helical cutting edges of the commoncutting inserts that comprise the at least one cutting flute.
 2. Thecutting tool system of claim 1, wherein the common cutting inserts eachcomprise two or more sinusoidal and helical cutting edges that areindexable in the insert pockets.
 3. The cutting tool system of claim 1,wherein the common cutting inserts each comprise two sinusoidal andhelical cutting edges that are indexable in the insert pockets.
 4. Thecutting tool system of claim 1, wherein the common cutting inserts eachcomprise four sinusoidal and helical cutting edges that are indexable inthe insert pockets.
 5. The cutting tool system of claim 1, furthercomprising an end-face cutting insert removably attachable to an insertpocket positioned at an engaging end of the tool holder, the end-facecutting insert having a shape that is different than a shape of theplurality of common cutting inserts.
 6. The cutting tool system of claim5, wherein the end-face cutting insert comprises a helical cutting edgethat helically aligns with the sinusoidal and helical cutting edges ofthe plurality of common cutting inserts forming the sinusoidal andhelical cutting edge of the at least one cutting flute.
 7. The cuttingtool system of claim 5, wherein the end-face cutting insert comprises asinusoidal and helical cutting edge that helically aligns with thesinusoidal and helical cutting edges of the plurality of common cuttinginserts forming the sinusoidal and helical cutting edge of the at leastone cutting flute.
 8. A cutting tool system comprising: a tool holdercomprising two or more series of common insert pockets, each series ofcommon insert pockets positioned in a helical orientation about alongitudinal axis of the tool holder; and a plurality of common cuttinginserts removably attachable to the common insert pockets in the toolholder to form two or more cutting flutes on the tool holder, the two ormore cutting flutes each comprising a helical grouping of the commoncutting inserts positioned in the insert pockets; wherein the commoncutting inserts each comprise at least one sinusoidal and helicalcutting edge; wherein two or more of the cutting inserts combine todefine a sinusoidal wavelength shape defined by one period per cuttinginsert; and wherein the two or more cutting flutes each comprise asinusoidal and helical cutting edge positioned about the longitudinalaxis of the tool holder and formed by alignment of the individualsinusoidal and helical cutting edges of the common cutting inserts thatcomprise the two or more cutting flutes.
 9. The cutting tool system ofclaim 8, wherein the common cutting inserts each comprise two or moresinusoidal and helical cutting edges that are indexable in the insertpockets.
 10. The cutting tool system of claim 8, wherein the commoncutting inserts each comprise two sinusoidal and helical cutting edgesthat are indexable in the insert pockets.
 11. The cutting tool system ofclaim 8, wherein the common cutting inserts each comprise foursinusoidal and helical cutting edges that are indexable in the insertpockets.
 12. The cutting tool system of claim 8, wherein adjacenthelical groupings of the common cutting inserts are offset relative toeach other along the longitudinal axis of the tool holder so that theinserts comprising adjacent helical flutes are not longitudinallyaligned in a cross sectional plane perpendicular to the longitudinalaxis.
 13. The cutting tool system of claim 8, further comprising two ormore end-face cutting inserts, each end-face cutting insert beingremovably attachable to an insert pocket positioned at an engaging endof the tool holder helically aligned with one of the two or more seriesof common insert pockets, and each end-face cutting insert having ashape that is different than a shape of the plurality of common cuttinginserts.
 14. The cutting tool system of claim 13, wherein the two ormore end-face cutting inserts each comprise a helical cutting edge thathelically aligns with the sinusoidal and helical cutting edges of theplurality of common cutting inserts forming the sinusoidal and helicalcutting edges of the two or more cutting flutes.
 15. The cutting toolsystem of claim 13, wherein the two or more end-face cutting insertseach comprise a sinusoidal and helical cutting edge that helicallyaligns with the sinusoidal and helical cutting edges of the plurality ofcommon cutting inserts forming the sinusoidal and helical cutting edgesof the two or more cutting flutes.
 16. The cutting tool system of claim13, wherein the two or more end-face cutting inserts have the sameshape, are differently sized, and are positioned in respective insertpockets with a common longitudinal clearance, so that adjacent helicalgroupings of the common cutting inserts are offset relative to eachother along the longitudinal axis of the tool holder so that the insertscomprising adjacent helical flutes are not longitudinally aligned in across sectional plane perpendicular to the longitudinal axis.
 17. Acutting insert comprising two or more sinusoidal and helical cuttingedges; wherein at least one of the two or more sinusoidal and helicalcutting edges defines one period of a sinusoidal wavelength shape. 18.The cutting insert of claim 17, wherein the cutting insert comprisesfour sinusoidal and helical cutting edges.
 19. A method for producing acutting tool system comprising: a tool holder comprising a plurality ofcommon insert pockets positioned in a helical orientation about alongitudinal axis of the tool holder; and a plurality of common cuttinginserts removably attachable to the plurality of common insert pocketsin the tool holder to form at least one cutting flute on the toolholder, the at least one cutting flute comprising a helical grouping ofcommon cutting inserts positioned in the insert pockets; wherein thecommon cutting inserts each comprise at least one sinusoidal and helicalcutting edge; the method comprising: positioning a cutting insert havinga sinusoidal-shaped cutting edge as if it were on the tool holder with ahelix angle; and modifying the sinusoidal shape of the cutting edge ofthe cutting insert to coincide with a cylindrical surface defined by acutting radius centered at a cutting axis of the cutting tool system;wherein two or more of the common cutting inserts combine to define asinusoidal wavelength shape defined by one period per cutting insert.20. The method of claim 19, further comprising: positioning a firstcommon cutting insert having a sinusoidal-shaped cutting edge as if itwere on a tool holder with a helix angle; positioning a second commoncutting insert having a sinusoidal-shaped cutting edge as if it were ona tool holder with a helix angle; rotating the second common cuttinginsert about the cutting axis of the cutting tool system whilemaintaining a constant cutting radius defined by the cutting toolsystem; and translating the second cutting insert parallel to thecutting axis while maintaining the constant cutting radius defined bythe cutting tool system.
 21. The method of claim 20, further comprising:successively positioning a plurality of common cutting inserts having asinusoidal-shaped cutting edge as if the cutting inserts were on a toolholder with a helix angle; successively rotating each of the pluralityof common cutting inserts about the cutting axis of the cutting toolsystem while maintaining the constant cutting radius defined by thecutting tool system; and successively translating each of the pluralityof cutting inserts parallel to the cutting axis while maintaining theconstant cutting radius defined by the cutting tool system.
 22. Themethod of claim 19, further comprising: positioning a seating surface ofa first insert pocket according to an assembly position of the firstcommon cutting insert having a sinusoidal-shaped cutting edge as if thefirst cutting insert were on a tool holder with a helix angle;positioning a seating surface of a second insert pocket according to anassembly position of the second common cutting insert having asinusoidal-shaped cutting edge as if the second cutting insert were onthe tool holder with a helix angle; rotating the seating surface of thesecond insert pocket about the cutting axis of the cutting tool systemwhile maintaining a constant cutting radius defined by the cutting toolsystem; and translating the seating surface of the second insert pocketparallel to the cutting axis while maintaining the constant cuttingradius defined by the cutting tool system.
 23. The method of claim 22,further comprising: positioning seating surfaces of a plurality ofinsert pockets according to assembly positions of a plurality of commoncutting inserts having a sinusoidal-shaped cutting edge as if theplurality of common cutting inserts were on the tool holder with a helixangle; successively rotating each of the seating surfaces of theplurality of insert pockets about the cutting axis of the cutting toolsystem while maintaining the constant cutting radius defined by thecutting tool system; and successively translating each of the seatingsurfaces of the plurality of insert pockets parallel to the cutting axiswhile maintaining the constant cutting radius defined by the cuttingtool system.